Foundations of Strategic Persistence - A Structural Theory of Competitive Systems Under Transformation

Classical game theory models strategic interaction between rational players. It presupposes that the players participating in the game remain sufficiently stable to sustain identities, strategies, payoff relations, and equilibria throughout interaction. This condition is not derived within game theory itself. La Profilée defines the persistence condition IR = R / (F · M · K) ≤ 1, where F denotes identity-bearing structure, M transformation-processing structure, K coordination between identity and transformation, and R transformation load. This paper establishes a structural theory of competitive systems under transformation. Strategic interaction does not merely alter payoffs. It alters the persistence conditions of the interacting systems themselves. Every strategic action changes transformation pressure, adaptive requirements, coupling structure, structural time, recoverability, and identity continuity across competitors. Competition therefore operates simultaneously on two levels: payoff optimization and persistence transformation. The central result is this: a strategic configuration can be payoff-rational, deviation-stable, and still persistence-destructive, anti-flourishing, or structurally transmutative. These conditions are independent and require separate analysis. Using a minimal three-player structure, the paper derives persistence transfer, persistence asymmetry, structural sacrifice, cooperation as persistence stabilization, persistence-inadmissible equilibrium, compensatory persistence, flourishing equilibrium, strategic transmutation, collapse propagation, recovery asymmetry, anti-flourishing selection, meta-competition, and strategic phase transitions as structural consequences of competitive interaction. Nash equilibrium is therefore shown to be insufficient as a criterion of strategic admissibility. Game theory describes strategic optimization within a game. La Profilée establishes the structural condition under which strategic systems can continue to exist, recover, flourish, or remain identifiable as the same systems at all.